When the elevator accelerates upward, the person's inertia resists this upward movement, which makes the person feel heavier. Notice that this value is greater than the that the person weighs while at rest. Plugging the relavent values into the above expression that we've derived will give us our answer. When the elevator accelerates upward, the elevator exerts a (normal) force on the individual that is equal in magnitude to the person's weight, but with reversed directionality.įinally, we can calculate the person's mass: The reason why the normal force gives us the person's weight is due to Newton's third law. Notice that we are solving for the new value of the normal force while the elevator is accelerating. Just as it was while at rest, the downward force acting on the individual in this case is still the force due to gravity, and the upward force acting on the individual is the normal force of the elevator's floor. In such a situation, there is now a net force acting on the individual, and that net upward force is due to the elevator's acceleration. Next, let's derive an expression while considering the upward acceleration of the elevator. The downward force acting on the individual is the force due to gravity, while the upward force is the normal force of the elevator's floor acting on the individual. Since there is no net force in the y-direction, that means that the upward forces must be exactly balanced by the downward forces. While at rest, there is no net force acting on this individual. In this situation, it's useful to picture a free-body diagram of the person and all of the forces acting on him/her. Let's begin our analysis by first considering the person to be at rest in the elevator. We're then asked to determine this person's new weight while they are undergoing this acceleration. In this question, we're presented with a scenario where a person weighing at rest is being accelerated upwards. This is an important property to know! When an object travels down a slope at a constant rate, the tangent of the angle of the slope is equal to the coefficient of kinetic friction. Also, the flatter the slope gets, the greater the normal force will become, hence the use of the cosine function.Ĭanceling out mass and solving for the angle on one side of the equation, we get: The flatter the slope gets, the less the force of gravity will have an effect on moving the block down the plane, hence the use of the sine function. If you are unsure of whether to use cosine or sine for each force, think about the situation practically.
Substituting in expressions for each force, we get: Since the block is traveling at a constant rate, we know the the gravitational and frictional force in the direction of the slope cancel each other out, and the net force is zero (there is no acceleration).
The first is gravity and the second is friction. There are two forces in play in this scenario.
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